Straight Line Graphs 1. Find the value of y if y=4x + 2 when x= 2 2. Here are four equations of straight lines: y= 2x +3, y= 3x, y=5 + 3x, y= 5x – 3 a. Which is the steepest line? b. Which line crosses the y axis at (0,3)? c. Which two lines are parallel? d. Which line goes through the origin? 3. Match the line to its equation y= 2x + 1 y= 2x – 3 y= ½x+ 1 y= 5 – ½x y= 5 4. Which of these points lie on the line y = 3x – 1: a) (3,-1) b) (2,5) c) (-1,3) d) (-2,-7) 5. a) Complete the table of values for y = 2x - 3 y x -2 -1 0 1 2 y -5 -3 x On the grid, draw the graph of y = 2x -3 Use your graph to find: i) the value of y when x = 1.7 ii) the value of x when y = -4.3 Substitution and Trial and Improvement 1. Find the output to the function machine if the input is 7. INPUT x3 - 1 OUTPUT. 2. If a = 3 what is 5a? 3. If b = 2c + 7, what is the value of b when c = 9? 4. Calculate the value of 5g – 4h when g = 3 and h = -4. 5. Find the value of 3(h + d) when h = 3 and d = -8. 6. What is the value of 3a2 when a = 4? 7. The following formula is used to cook a joint of meat in the oven: t = 12w + 15, where w is the weight in pounds and t is the time in minutes. How long would it take to cook a joint of meat weighing 6 pounds? 8. Find a whole number solution to: n2 + 2n + 3 = 66. 9. Use the method of trial and improvement to find a solution to 1 decimal place, of the equation x3 + x = 100. Area and perimeter State the units for all answers 1. (a) Find the area (b) Find the perimeter 2. What is the area of this triangle? 3. Find a. the area b. the perimeter of this right angled triangle. 4. Find the area of this isosceles triangle. 5. The diagram below shows a triangular roof with a rectangular skylight. What is the area of the shaded roof? Simplify, Expand and Factorise 1. Simplify 4x + 2x + x 2. Simplify 8a + 3b – 5a + 2b + 12 3. Multiply out 3(5c – 2d) 4. Multiply out and simplify 4(3e – f) + 7(e + 2f) 5. Factorise 12c + 8d 6. Factorise 15e – 5f 7. Multiply out and simplify 3(5e – 2f) – 4(2e + f) 8. Multiply out and simplify 6(2e – 3f) – 2(5e – 10f) 9. Multiply out y(y + 3) 10. Multiply out 2y(4y – 3) 11. Factorise as completely as possible x2 – 5x 12. Factorise as completely as possible 6x2 + 3x 13. Factorise as completely as possible 5q2 – 15q3 Real-life graph The conversion graph above can be 80 used for changing between gallons and litres. 70 (i) Use the graph to change 11 60 gallons to litres. 50 (ii) Use the graph to change 35 litres to gallons. Litres 40 30 Last week David’s car used 27 1 2 gallons of petrol. 20 David paid 70p for each litre of 10 petrol. 0 (b) Work out how much David paid 0 5 10 15 20 for 27 1 gallons of petrol. 2 Gallons 2. Here is part of a travel graph of Siân’s journey from her house to the shops & back. 20 18 16 Distance in km 14 from 12 Siân’s house 10 8 6 4 2 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Time in minutes (a) Work out Siân’s speed for the first 30 minutes of her journey. Give your answer in km/h. Siân spends 15 minutes at the shops. She then travels back to her house at 60 km/h. (b) Complete the travel graph. Sequences 1. Here are some patterns made from matchsticks: Pattern Pattern Pattern number 1 number 2 number 3 (a) Complete this table for the pattern sequence Pattern number 1 2 3 4 5 Number of matchsticks 4 7 10 used (b) How many matchsticks are used in pattern number 15? Asif says that if there are m matchsticks in pattern number n then the formula for m in terms of n is m = 4n. (c) Explain why Asif’s formula is not correct. 2. Here are the first 5 terms of a number pattern. 3 7 11 15 19 (a) Write down the next two numbers of the sequence. (b) Write down, in words, the rule to continue this sequence. (c) Find, in terms of n, an expression for the nth term of the sequence. (d) Find the 50th term of the sequence. 3) The expression n(n+1) is the nth term of the sequence of triangular numbers 2 1, 3, 6, 10, ... Write down an expression, in terms of n, for the nth term of the sequence 10, 30, 60, 100, ... Constructions and loci 1. Measure this line accurately 2. Draw the net of a cube of side 3cm. 3. Use your compasses to draw a triangle with lengths 7cm, 9cm and 10cm. 4. Measure the angles in your triangle as accurately as you can. 5. Use your protractor to draw a triangle of base 8 cm and angles of 450 and 600 6. A rectangular garden measures 12m by 10m. Draw a scale diagram of the garden. 7. A tree is planted in the exact centre of the garden. Show the tree on your diagram. Explain how you decided where to place the tree. 8. The gardener wants to seed the garden with grass. She cannot seed within 3m of the tree nor within 1m of the garden fence. Show accurately where she can put the seed. Volume What is the volume of this shape? Represent The diagram shows a box in the shape of a cuboid. 10 cm Work out the volume of the box. 4 cm 12 cm Diagram NOT Calculate the volume accurately drawn of the triangular 5 cm prism 4 cm 7 cm 3 cm Dia A can of drink is in the shape accu of a cylinder. The can has a radius of 4 cm and a height of 15 cm. 15 cm Calculate the volume of the cylinder. Give your answer correct to 3 significant figures 4 cm Measures and Conversions Look up the conversion rates in your revision book, planner or the internet. 1. Calculate 3.1 x 100 2. Convert 5 metres into centimetres. 3. a) Find the area of the square of side 1m b) Convert your answer to square centimetres 4. Convert 5 square metres into square centimetres. 5. a) Convert 5 cubic metres into cubic centimetres. b) How many litres would this be? 6. Approximately how many centimetres is 3 inches? 7. How many lbs in 3 kg? 8. How many kms is 5 miles? 9. If $1.80 = £1, how much is $5? Pythagoras 1. What name is given to the longest side in a right-angled triangle? 2. What is the value of 42? 3. What is the value of 144? 4. I know the two shortest sides of a right-angled triangle. Explain how I find the length of the longest side 5. Calculate the length of x Answer correct to 1 decimal place 5cm x 4cm A Triangle ABC is isosceles AB = AC 6. BC = 10cm The height of triangle ABC is 7cm C Calculate the length of AB B Solving Equations 1. Find the value of x if x+2=7 2. Find the value of a when a – 6 = 15 3. Solve for y: 2y = 10 4. Find c in 8c = 28 5. Find the solution of 3p – 5 = 7 6. Solve for t : 4t + 7 = -1 7. Find the solution to 2(m + 3) = 18 8. Find n in 3(4n – 2) = 18 9. Find x in 5x – 3 = 2x + 9 10. Find the solutions to the following equations: a. 5t + 9 = 84 t = ……………. b. 6k + 7 = 2k - 29 k= …………… c. 5(4x + 1) = 55 x = …………….. Speed, Distance and Time 1. Convert to hours and minutes a. 2.25 hours b. 1.8 hours c. 3.55 hours 2. Convert to hours a. 30 mins b. 1 hour 45 mins c. 2 hours 21 mins 3. A car travels at 30 miles per hour, how far does it travel a. in 4 hours b. 30 minutes 4. A Jumbo jet takes 6 hours to fly from London to Athens, a distance of 2400km. Calculate the average speed of the Jumbo Jet. Clearly state the units of your answer. 5. Ali lays 150 floortiles every hour. He always works at the same speed. How long would it take Ali to lay 570 floortiles Give your answer in hours and minutes. 6. A sprinter runs 200m in 20.42 seconds Estimate his average speed in kilometres per hour. Angles 1. What do the angles in a triangle add up to? 2. What do the angles in a quadrilateral add up to? 3. Calculate the angle marked x. Show your working. 1230 x0 4. State the angle y. Give a reason for your answer. 670 yo 5. (a) (i) Work out the size of angle p (ii) Give a reason for your answer (b) (i) Work out the size of angle q (ii) Give reasons for your answer Transformations (1) 1. Reflect shape A in the line shown. 2. Reflect shape B in the x-axis 3. Rotate shape C through 180 about point X Transformations (2) 1. Circle the correct statement: (a) Shape F is formed by reflecting shape E through 180 clockwise about the point (1,1) (b) Shape F is formed by rotating shape E through 90 clockwise about the point (1,1) (c) Shape F is formed by rotating shape E through 180 clockwise about the point (1,1) 2. Complete the statement: Shape H is an …………………………………. of shape G with scale factor ………… and centre of enlargement (………. , …………) 3. Below is a diagram showing how shape A has been transformed into shape C. (i) Describe as fully as you can the single transformation which takes shape A onto shape B. (ii) Describe as fully as you can the single transformation which takes shape A onto shape C.